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Integrable sigma models and 2-loop RG flow

A preprint version of the article is available at arXiv.

Abstract

Following arXiv:1907.04737, we continue our investigation of the relation between the renormalizability (with finitely many couplings) and integrability in 2d σ- models. We focus on the “λ-model,” an integrable model associated to a group or symmetric space and containing as special limits a (gauged) WZW model and an “interpolating model” for non-abelian duality. The parameters are the WZ level k and the coupling λ, and the fields are g, valued in a group G, and a 2d vector in the corresponding algebra. We formulate the λ-model as a σ-model on an extended G × G × G configuration space (g, h,\( \overline{h} \)), defining h and \( \overline{h} \) by A+ = h∂+h1, A_ = \( \overline{h} \)∂−\( \overline{h} \)1. Our central observation is that the model on this extended configuration space is renormalizable without any deformation, with only λ running. This is in contrast to the standard σ-model found by integrating out A±, whose 2-loop renormalizability is only obtained after the addition of specific finite local counterterms, resulting in a quantum deformation of the target space geometry. We compute the 2-loop β-function of the λ-model for general group and symmetric spaces, and illustrate our results on the examples of SU(2)/U(1) and SU(2). Similar conclusions apply in the non-abelian dual limit implying that non-abelian duality commutes with the RG flow. We also find the 2-loop β-function of a “squashed” principal chiral model.

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Correspondence to Nat Levine.

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ArXiv ePrint: 1910.00397

Arkady A. Tseytlin also at the Institute of Theoretical and Mathematical Physics, MSU and Lebedev Institute, Moscow.

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Hoare, B., Levine, N. & Tseytlin, A.A. Integrable sigma models and 2-loop RG flow. J. High Energ. Phys. 2019, 146 (2019). https://doi.org/10.1007/JHEP12(2019)146

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Keywords

  • Integrable Field Theories
  • Renormalization Group
  • Sigma Models